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IEEE POWER ELECTRONICS REGULAR PAPER 1
Natural Boundary Transition and Inherent Dynamic
Control of a HybridMode Modulated
DualActiveBridge Converter
Jingxin Hu, Member, IEEE, Shenghui Cui, Member, IEEE, Rik W. De Doncker, Fellow, IEEE
Abstract—This article proposes a hybridmode modulation
strategy for the singlephase dualactivebridge (DAB) dcdc con
verter that realizes softswitching in the whole operating range.
Different from existing modulation methods that are usually
dependent on complex mathematical optimization processes, the
presented study reveals that the simple trapezoidal continuous
conduction mode and triangular discontinuous conduction mode
inspired by a quasisingleactivebridge operation can naturally
and sequentially extend the softswitching boundary of the
conventional singlephaseshift (SPS) modulation to the full range
in both the buck and boost modes. Meanwhile, the transformer
rms current is also reduced. Moreover, a fastdynamic control
with inherent seamless mode transitions is realized by intro
ducing the predictivecurrent SPS modulation. The proposed
hybridmode modulation strategy with closedform solutions can
be easily implemented in a generalized closedloop controller,
which enables an ultrawidevoltagerange operation of the DAB
converter with signiﬁcantly elevated efﬁciency and fast transient
responses. The effectiveness of the proposed method is validated
by comprehensive experimental results from a smallscale DAB
prototype.
Keywords—Dualactivebridge, dynamic control, modulation
schemes, singleactivebridge, smooth transition, softswitching,
wide operating voltage range.
I. INTRODUCTION
THE dualactivebridge (DAB), ﬁrst proposed in 1988 for
aerospace applications [1], [2], is one of the most popular
bidirectional isolated dcdc converter topologies. Due to its
attractive features such as inherent softswitching capability,
buck and boost operation, and high power density, it is ideal
for dc solidstate transformers in grid applications [3]–[6], re
newable energy integration [7], [8], energy storage systems [9]
as well as moreelectric transportation systems [10]–[13].
The singlephaseshift (SPS) is the original and mean
while the simplest modulation method for the DAB con
verter [2]. With adequate inductive reactive currents in the
highfrequency aclink transformer, all power semiconductor
devices can realize zerovoltage switching (ZVS), which leads
Manuscript received June 1, 2021, revised August 27, 2021 and accepted
October 10, 2021. Date of publication October xx, 2021; date of current
version xx xx, xx. (Corresponding author: Shenghui Cui)
Jingxin Hu and Rik W. De Doncker are with the Institute for Power Gen
eration and Storage Systems, E.ON ERC and FEN Research Campus, RWTH
Aachen University, Aachen 52074, Germany (email: jhu@eonerc.rwth
aachen.de; post pgs@eonerc.rwthaachen.de).
Shenghui Cui is with Department of Electrical and Computer Engi
neering, Seoul National University, Seoul 08826, South Korea (email:
cuish@snu.ac.kr).
This work is supported by European Union’s Horizon 2020 research
and innovation programme under grant agreement No. 957788, project HY
PERRIDE, and the Federal Ministry of Education and Research (BMBF,
FKZ03SF0490), Flexible Electrical Networks (FEN) Research Campus.
to highefﬁciency operation and clean switching waveforms
with low electromagnetic interference (EMI). However, when
the outputtoinput voltage ratio deviates greatly from unity
especially under lightload conditions, the DAB converter
will not only lose softswitching but also suffer from high
rms current. Thus, despite its advantages under the nominal
operating condition, the SPS modulation is not sufﬁcient to
guarantee highefﬁciency operation of the DAB converter in
the full operating range.
To address this issue, several alternative modulation
schemes with adjustable duty ratios of the input and output
ac voltages have been proposed in literature, which are com
prehensively summarized in [14]. In [15], [16], the extended
phaseshift (EPS) modulation is proposed, which can realize
softswitching in the full operating range. However, the EPS
modulation still suffers from a relatively high rms current un
der lightload conditions. Moreover, due to lack of closedform
solutions, the EPS modulation usually has to be implemented
in lookuptables, which has considerable constraints in prac
tical applications. To improve the applicability of this method,
the fundamentaloptimal strategy (FOPS) is proposed in [17],
which can be implemented in a uniﬁed controller with simple
calculations. However, the maximum power transfer capability
and the softswitching range are compromised. In [18], the
dualphaseshift (DPS) modulation is proposed to eliminate the
reactive power and boost the system efﬁciency. Unfortunately,
it cannot realize fullrange softswitching. Besides, similar
to the EPS, the DPS modulation also lacks a closedform
solution to its control variables. The triplephaseshift (TPS)
modulation presented in [19], [20] inherently provides sufﬁ
cient degrees of freedom to extend the softswitching range
and meanwhile reduce the rms current. However, it consists
of many possible switching modes which complicates the
parameter determination. The optimal switching pattern and
control variables of the TPS modulation are normally derived
from complex mathematical optimization process [21]–[25].
This usually results in a hybridmode operation, which is
not intuitive due to lack of physical insights in the circuit.
Moreover, modulationmode transitions under transient oper
ation conditions can induce a transient dcbias current in the
highfrequency aclink transformer. This can highly degrade
the dynamic performance of the converter or even cause the
transformer core saturation. Although the transient dcbias can
be suppressed by dedicated control methods [26]–[30], this
usually requires sophisticated gating logic and increases the
computational complexity of the hybridmode operation.
Distinguished from the aforementioned methods, this article
proposes a hybridmode modulation strategy that is inspired
IEEE POWER ELECTRONICS REGULAR PAPER 2
by the quasisingleactivebridge operation. The analysis ﬁrst
reveals that the ZVS boundary of the SPS modulation in
the buck mode can be naturally and sequentially extended to
the full operating range by the continuous and discontinuous
conduction modes of the singleactivebridge (SAB) converter.
The switching patterns of the DAB converter are then designed
to emulate the operation waveforms of the SAB converter
in both buck and boost mode respectively, which can cover
the whole hardswitching region of the SPS modulation with
softswitching and reduced rms current. The resulting hybrid
mode modulation not only has a natural boundary transition,
but also beneﬁts from closedform solutions, which enables
simple modelbased control implementation. Moreover, with
the predictivecurrent SPS modulation, the proposed hybrid
mode modulation can realize inherent dynamic control and
smooth mode transitions without transient dcbias current.
Notice that the fastdynamic control does not require any
additional gating logic under transient operation conditions,
which minimizes the complexity of the control algorithm.
Thus, with the proposed method, the DAB converter can
operate in an ultrawide voltage range with both a high
efﬁciency and a fast transient response.
It is worth mentioning that the motivation of this paper is
not to provide another globally optimized modulation method
for the DAB converter, but to reveal a simple and intuitive
hybridmode modulation method based on the intrinsic circuit
behaviors. Notice that it is also possible to emulate the opera
tion of a asymmetricaldualactivebridge (ADAB) [31], [32],
also known as semidualactivebridge (SDAB) [33], which
has more control freedoms to optimize the performance than
the SAB converter. However, due to multiple control variables,
the ADAB converter still requires a complex optimization pro
cedure for modulation schemes and dedicated dynamic control
methods to suppress transient dcbias currents. Therefore, the
ADAB operation is not considered in this paper.
The rest of the article is structured as follows. First, the
proposed hybridmode modulation schemes, are introduced
in Section II with their origin from the SAB operation and
the corresponding closedform solutions. This is followed
by a description of the inherent dynamic control and the
implementation of the uniﬁed voltage control in Section III.
Furthermore, in Section IV, the proposed modulation and
control methods are veriﬁed by comprehensive experimental
results from a smallscale laboratory prototype. Finally, Sec
tion V concludes this article.
II. MODULATION SCHEMES
The singlephase DAB converter consists of two Hbridges
linked by a highfrequency ac transformer, as depicted in
Fig. 1. The total leakage inductance 𝐿𝜎is employed as
the energy transfer element, whose current is driven by the
difference between the ac voltages of the input and output
bridges, i.e. 𝑣AB and 𝑣CD, respectively. The DAB converter
normally has three control variables, which are the duty ratios
𝐷pand 𝐷sof the input and output ac voltages respectively,
and the phaseshift ratio 𝐷𝜑between two bridges.
ip
S1
ABCD
Lσ
S2
S3
S4
Q1
Q2
Q3
Q4
is,dc
isC
iload
Fig. 1: Circuit diagram of singlephase DAB converter.
0Ts/2 Ts
0
DpTs
ip
is,dc
is,dc
0
0Ts/2 Ts
0
DpTs
ip
is,dc
is,dc
0
DsTs
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
(a) (b)
(c)
ZVS Region
HardSwithing
Input Bridge
HardSwithing
Output Bridge
1
23
DsTs
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
Fig. 2: Key operation waveforms and characteristics of the SPS modulation.
(a) Typical ZVS operation waveforms; (b) Operation waveforms at the ZVS
boundary in the buck mode; (c) ZVS region.
A. SinglePhaseShift Modulation and Its ZVS Boundary
As the original method, the SPS modulation is still one
of the most commonly used operation schemes for the DAB
converter due to its simplicity. As shown in Fig. 2(a), in the
SPS modulation, 𝐷pand 𝐷sare ﬁxed to 0.5, and only 𝐷𝜑is
employed as the control variable to change the power ﬂow. For
sake of simplicity, only the positive power ﬂow is hereinafter
considered. The transformer current 𝑖pcan be expressed by
piecewise linear functions [2], whereby the averaged output
dc current 𝐼s−dc and its maximum value are calculated as
𝐼s,dc =
𝑁tr𝑉p𝐷𝜑(1−2𝐷𝜑)
𝑓 𝐿 𝜎
,(1)
𝐼s,dc,max =
𝑁tr𝑉p
8𝑓 𝐿 𝜎
,at 𝐷𝜑=0.25.(2)
where 𝑁tr denotes the turns ratio of the transformer, 𝑉pdenotes
the input dc voltage, and 𝑓denotes the switching frequency.
According to (1), in the SPS modulation, 𝐼s,dc is independent
of the output dc voltage 𝑉s. Furthermore, 𝐷𝜑is calculated by
𝐷𝜑=
1
4· 1−1−8𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p!.(3)
IEEE POWER ELECTRONICS REGULAR PAPER 3
ip
S1
ABCD
Lσ
S2
S3
S4
Q1
Q2
Q3
Q4
is,dc
isC
iload
Fig. 3: Circuit diagram of singlephase SAB converter.
When the transformer current ﬂows into the antiparallel
diodes at the turnon instant of the corresponding switch, ZVS
turnon is realized. This leads to the softswitching condition
𝑖p(0)=(𝑑−1−4𝑑𝐷 𝜑)𝑉p
4𝑓 𝐿 𝜎≤0,for input bridge,
𝑖p(𝐷𝜑𝑇s)=(4𝐷𝜑−1+𝑑)𝑉p
4𝑓 𝐿 𝜎≥0,for output bridge,
(4)
where 𝑑=𝑁tr𝑉s/𝑉pdenotes the dc voltage ratio, and 𝑇s=1
/𝑓
denotes the switching period.
Fig. 2(b) depicts the operation waveforms under the ZVS
boundary condition of the SPS modulation in buck mode
(𝑑 < 1), where the switches in the output bridge realize zero
currentswitching (ZCS) turnoff. Substituting (4) into (1), the
ZVS boundary of the SPS modulation can be identiﬁed in (5),
which is also shown in Fig. 2(c). It can be observed that, in
the SPS modulation, the DAB converter realizes softswitching
when the voltage ratio is close to unity and the load current
is relatively high. Moreover, the hardswitching regions of the
output bridge and the input bridge are located in the buck
mode (𝑑 < 1) and the boost mode (𝑑 > 1), respectively.
𝐼s,dc ≥𝑁tr𝑉p(𝑑2−1)
8𝑓 𝐿 𝜎𝑑2,for input bridge,
𝐼s,dc ≥𝑁tr𝑉p(1−𝑑2)
8𝑓 𝐿 𝜎
,for output bridge.
(5)
B. Operation Boundary of a SingleActiveBridge Converter
When the gating signals of the switches in the output bridge
are disabled, the output bridge operates as a diode rectiﬁer. The
circuit topology effectively turns into a singlephase single
activebridge (SAB) converter as depicted in Fig. 3. The SAB
is a unidirectional isolated bucktype dcdc converter, which
regulates the power ﬂow by adjusting the duty ratio 𝐷pof
the input ac voltage [2]. Due to the existence of the output
diode rectiﬁer, the transformer current is always in phase with
the output ac voltage, which leads to the ZCS turnoff of the
diode rectiﬁer. Dependent on the load condition, the SAB con
verter can operate in either the continuous conduction mode
(CCM) or the discontinuous conduction mode (DCM) [34]–
[36], which are described in detail as follows. Since the output
bridge is not switched in the SAB converter, the variables 𝐷𝜑
and 𝐷sin Section IIB represent the equivalent external and
internal phaseshift ratios judged from the voltage waveforms
of the SAB converter.
1) CCM: The SAB converter operates in the CCM at a
relatively high load current. As depicted in Fig. 4(a), the
input ac voltage 𝑣AB leads the output ac voltage 𝑣CD with an
equivalent phaseshift ratio 𝐷𝜑≥0. The transformer current
0Ts/2 Ts
0
DpTs
t1t2
ip
is,dc
is,dc
0
SAB
DsTs
S1S2
S3S4
S4
Q1, Q4Q2, Q3
DAB
0Ts/2 Ts
t1t2
SAB
S1S2
S3
S4
Q1Q2
DAB
S4
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
DφTs
(a) (b)
Fig. 4: Key operation waveforms of the SAB converter and the quasiSAB
operation in the buck mode. (a) Trapezoidal continuous conduction mode
(buck); (b) Triangular discontinuous conduction mode (buck).
is continuous with a trapezoidal waveform. Therefore, it is
hereinafter named as trapezoidal CCM (TZCCMBuck). In
the TZCCMBuck mode, the equivalent duty ratio 𝐷sof
the output bridge is always 0.5. The input bridge can realize
ZVS turnon, while the output bridge can realize ZCS turn
off. Therefore, hardswitching with a diode reverse recovery
is avoided under this condition.
The transformer current of the TZCCMBuck mode can
also be expressed by piecewise linear functions [2]. The
expression of 𝐷𝜑is given by
𝐷𝜑=
1−𝑑
4,(6)
which is only related to the voltage ratio 𝑑.
The relationship between 𝐼s,dc and 𝐷pis described as:
𝐼s,dc =
𝑁tr𝑉p(−4𝐷2
p+4𝐷p−𝑑2)
8𝑓 𝐿 𝜎
.(7)
Thereby, 𝐷pis calculated as
𝐷p=
1
2−1−𝑑2
4−2𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p
.(8)
For a given voltage ratio 𝑑, the maximum output dc current
is obtained at 𝐷p=0.5, while the minimum output dc
current is obtained at 𝐷p=𝑑
2. Therefore, the upper and lower
boundaries of the TZCCMBuck mode are deﬁned as
𝐼s,dc,max =
𝑁tr𝑉p(1−𝑑2)
8𝑓 𝐿 𝜎
,(9a)
𝐼s,dc,min =
𝑁tr𝑉p𝑑(1−𝑑)
4𝑓 𝐿 𝜎
,(9b)
which are plotted in Fig. 5. Comparing (5) and (9a), one can
easily identify that the upper boundary of the TZCCMBuck
mode is also the ZVS boundary of the SPS modulation in the
buck mode, where the operation waveforms of two modes are
identical as shown in Fig. 2(b).
2) DCM: The SAB converter operates in the DCM at a
lower load current. The transformer current is discontinuous
with a triangular waveform, as depicted in Fig. 4(b). Therefore,
it is hereinafter named as triangular DCM (TRDCMBuck).
In the TRDCMBuck mode, 𝐷schanges with 𝐷paccording to
IEEE POWER ELECTRONICS REGULAR PAPER 4
ZVSSPS
1
2a
TZCCM
(buck)
2b
TRDCM
(buck)
3a
TZCCM
(boost)
3b
TRDCM
(boost)
Eq.(9a)
Eq.(9b)
Eq.(15a)
Eq.(15b)
Eq.(2)
Fig. 5: Operation range of the proposed hybridmode modulation.
𝐷s=
𝐷p
𝑑.𝐷𝜑is deﬁned as 𝐷𝜑=
𝐷s−𝐷p
2=𝐷s(1−𝑑)
2. As shown
in Fig. 4(b), half of the switches in the input bridge can realize
ZVS turnon, and the other half can realize ZCS turnoff as
the output bridge. Therefore, no hardswitching operation with
a diode reverse recovery occurs under this condition.
The average output dc current with its maximum and
minimum values is given by
𝐼s,dc =
4𝑁tr𝑉p𝑑𝐷2
𝜑
(1−𝑑)𝑓 𝐿 𝜎
,(10)
𝐼s,dc,max =
𝑁tr𝑉p𝑑(1−𝑑)
4𝑓 𝐿 𝜎
,at 𝐷𝜑=
1−𝑑
4,(11a)
𝐼s,dc,min =0,at 𝐷𝜑=0.(11b)
From (10), 𝐷𝜑is calculated as
𝐷𝜑=(1−𝑑)𝑓 𝐿 𝜎𝐼s,dc
4𝑑𝑁tr𝑉p
.(12)
The operation range of the TRDCMBuck mode is depicted
in Fig. 5, which has a natural boundary transition from the
TZCCMBuck mode. Fig. 6 further shows the operation
waveforms under the boundary condition. Therefore, with a
combination of the TZCCMBuck, TRDCMBuck and SPS
modulation modes, as depicted in Fig. 5, the DAB converter
can realize fullrange softswitching in the buck mode.
Although the SAB operation can extend the softswitching
range of the DAB converter, it also has several constraints:
1) In the TRDCMBuck mode, the operation state of the
output diode rectiﬁer is undeﬁned in the zerocurrent interval,
which will result in a highfrequency oscillation of 𝑣CD due to
parasitics in the circuit. This can potentially cause EMI issues.
2) If unipolar transistors, e.g. MOSFETs, are employed, the
SAB operation cannot take the advantage of the synchronous
rectiﬁcation to reduce the conduction loss in the output bridge.
3) Most importantly, the SAB operation is only valid in the
buck mode.
C. Proposed HybridMode Modulation with Natural Bound
ary Transition
To tackle these issues, a hybridmode modulation is pro
posed for the DAB converter to imitate the SAB operation in
the whole hardswitching region of the SPS modulation.
0t2=Ts/2 Ts
t1
SAB
S1S2
S3
S4
Q1Q2
DAB
S4
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
Fig. 6: Operation waveforms of the boundary condition between the TZ
CCMBuck and TRDCMBuck modes.
(a) (b)
0Ts/2 Ts
0
t1t2
ip
is,dc
is,dc
0DsTs
S1, S4S2, S3
Q3
Q4
DφTs
DpTs
Q1Q2
0Ts/2 Ts
t1t2
S1S2
S3
S4
Q1Q2
Q4Q3
is,dc
is,dc
DpTs
DsTs
DφTs
ip
0
0
Fig. 7: Key operation waveforms in the boost mode. (a) Trapezoidal continu
ous conduction mode (boost); (b) Triangular discontinuous conduction mode
(boost).
1) TZCCMBuck and TRDCMBuck: In the buck mode,
the same TZCCMBuck and TRDCMBuck modes are em
ployed except for applying the synchronous rectiﬁcation tech
nique. As shown in Fig. 4, according to the derived closed
form solutions in Section IIB, the devices in the output
bridge are switched to generate exactly the same ac voltage
waveform as the SAB converter in these two modes. Thus,
the output bridge can not only maintain ZCS turnoff, but
also reduce the conduction loss due to lower onstate voltage
of MOSFETs than the forward voltage of diodes. Moreover,
since a zerovoltage state is deﬁned for 𝑣CD in the zerocurrent
interval in the TRDCMBuck mode, the EMI issue due to
an oscillating ac voltage can be avoided. It should be also
noticed that the TZCCMBuck and TRDCMBuck modes
are effectively special conditions of the EPS modulation and
the TPS modulation, respectively.
2) TZCCMBoost and TRDCMBoost: To achieve the
similar operation performance in the boost mode, the TZ
CCMBuck and TRDCMBuck modes are mirrored and
modiﬁed to the TZCCMBoost and TRDCMBoost modes,
respectively, as depicted in Fig. 7.
As shown in Fig. 7(a), the TZCCMBoost mode maintains
a continuous trapezoidal current waveform. However, as a
mirrored version of the TZCCMBuck mode, 𝐷pis ﬁxed to
0.5, while 𝐷salong with 𝐷𝜑is adapted to realize ZCS turn
off of the switches in the input bridge. Meanwhile, the output
bridge can realize ZVS turnon. The transformer current can
IEEE POWER ELECTRONICS REGULAR PAPER 5
be similarly expressed in piecewise linear functions. The ZCS
turnoff condition of 𝑖p(0)=𝑖p(𝑇s
2)=0yields
𝐷𝜑=
𝑑−1
4𝑑(13)
The averaged output dc current with its maximum and
minimum values of the TZCCMBoost mode is given by
𝐼s,dc =
𝑁tr𝑉p(−4𝑑2𝐷2
s+4𝑑2𝐷s−1)
8𝑑2𝑓 𝐿 𝜎
,(14)
𝐼s,dc,max =
𝑁tr𝑉p(𝑑2−1)
8𝑑2𝑓 𝐿 𝜎
,at 𝐷s=
1
2,(15a)
𝐼s,dc,min =
𝑁tr𝑉p(𝑑−1)
4𝑑2𝑓 𝐿 𝜎
,at 𝐷s=
1
2𝑑.(15b)
From (14), 𝐷sin the TZCCMBoost mode is obtained by
𝐷s=
1
2−𝑑2−1
4𝑑2−2𝑓 𝐿 𝜎𝐼s,dc
𝑁tr𝑉p
.(16)
According to (15a) and (15b), the operation region of the
TZCCMBoost mode is depicted in Fig. 5, which transits
naturally from the ZVS boundary of the SPS modulation.
The last remaining piece of the hardswitching region in
Fig. 5 is ﬁnally covered by the TRDCMBoost mode, which
is derived by mirroring the switching pattern of the TRDCM
Buck mode as depicted in Fig. 7(b). To realize the desired
discontinuous triangular current waveform, 𝐷p=𝑑𝐷sneeds
to be maintained. Thus, 𝐷𝜑is deﬁned as 𝐷𝜑=(𝑑−1)𝐷s
2. In
this mode, half of the switches in the output bridge can realize
ZVS turnon, while the remaining switches in both the input
and output bridges can realize ZCS turnoff.
The averaged output dc current with its maximum and
minimum values of the TRDCMBoost mode is given by
𝐼s,dc =
4𝑁tr𝑉p𝐷2
𝜑
(𝑑−1)𝑓 𝐿 𝜎
,(17)
𝐼s,dc,max =
𝑁tr𝑉p(𝑑−1)
4𝑓 𝐿 𝜎𝑑2,at 𝐷𝜑=
𝑑−1
4𝑑,(18a)
𝐼s,dc,min =0,at 𝐷𝜑=0.(18b)
From (10), 𝐷𝜑in the TRDCMBoost mode is obtained by
𝐷𝜑=(𝑑−1)𝑓 𝐿 𝜎𝐼s,dc
4𝑁tr𝑉p
.(19)
The operation region of the TRDCMBoost mode is de
picted in Fig. 5, which further extends the softswitching range
towards noload conditions with a natural boundary transition
from the TZCCMBoost mode.
Therefore, combining the SPS, TZCCMBuck, TRDCM
Buck, TZCCMBoost and TRDCMBoost modes, the DAB
converter can realize fullrange softswitching with seamless
mode transitions. It is worth mentioning that the natural bound
ary transition is not only for the output dc current, but also for
control variables in the switching patterns as depicted in Fig. 8.
It is shown that in both the buck and boost modes the control
variables, i.e. 𝐷𝜑,𝐷pand 𝐷s, change continuously between
two adjacent modulation modes. Moreover, according to the
derived expressions of the rms current for these modulation
TRDCMBuck TZCCMBuck SPS TRDCMBoost TZCCMBoost SPS
(a) (b)
Fig. 8: Control variables 𝐷𝜑,𝐷pand 𝐷sof the proposed modulation method
at a variable output dc current. (a) At 𝑑=0.5. (b) At 𝑑=1.5.
dc
dc
Fig. 9: Ratio between the rms current and the output dc current in the whole
operating range.
TABLE I: Expressions of the transformer rms current in different modulation
modes.
Mode Expression of 𝐼p,rms
SPS √3𝑁tr𝑉p
12 𝑓 𝐿𝜎−64𝑑 𝐷3
𝜑+48𝑑𝐷 2
𝜑+ (𝑑−1)2
TZCCMBuck √3𝑁tr𝑉p
6𝑓 𝐿𝜎−(2𝐷p−𝑑)3
2+ (𝑑−1)2(3(2𝐷p−𝑑)2
4+3(2𝐷p−𝑑)
2+𝑑2)
TRDCMBuck 4𝑁tr𝑉p𝑑𝐷 𝜑
𝑓 𝐿𝜎𝐷𝜑
3(1−𝑑)
TZCCMBoost √3𝑁tr𝑉p
6𝑑 𝑓 𝐿𝜎−𝑑(2𝑑 𝐷s−1)3
2+ (𝑑−1)2(3(2𝑑 𝐷s−1)2
4+3(2𝑑𝐷s−1)
2+1)
TRDCMBoost 4𝑁tr𝑉p𝐷𝜑
𝑓 𝐿𝜎𝑑 𝐷𝜑
3(𝑑−1)
modes as given in Table. I, the large rms current in the
hardswitching region of the SPS modulation is signiﬁcantly
reduced by the proposed hybridmode modulation method, as
depicted in Fig. 9.
III. INHERENT DYNAMIC CONT ROL
When the DAB converter operates under transient condi
tions, the switching pattern along with its control variables
𝐷p,𝐷sand 𝐷𝜑can dynamically change, which leads to
either a state change in the same modulation mode or a
mode transition. When the initial steadystate currents of two
consecutive switching patterns are different, a transient dc
bias is induced in the transformer current. This can result in
degraded transient performance or even cause transformer core
saturation. Therefore, the dynamic current control is necessary
for the hybridmode operation of the DAB converter.
The aforementioned CCM and DCM in both the buck and
boost modes have a common feature, which is ZCS turnoff of
the switches. Therefore, it is convenient to align the starting
IEEE POWER ELECTRONICS REGULAR PAPER 6
0Ts/2 Ts
0
ip
is,dc
is,dc
0
(a)
Ts/2 Ts
ip
S1S2
Q1Q2
S4S3
Q4Q3
0
Ts/2
Ts
S1S2
S3
S4
Q1Q2
Q4Q3
0
TRDCMBuck SPS
(b)
tx
S1, S4S2, S3
Q1, Q4Q2, Q3
DφTs
Fig. 10: Key operation waveforms of the inherent dynamic control. (a)
Predictivecurrent SPS modulation; (b) Mode transition from the TRDCM
Buck to the predictivecurrent SPS modulation.
instant of the switching pattern with a ZCS turnoff instant in
each switching cycle. Speciﬁcally, the starting instant of the
switching period in both the TZCCMBuck and TRDCM
Buck modes is aligned with the rising edge of the positive 𝑣CD
at 𝑖p=0, as depicted in Fig. 4. For the TZCCMBoost and
TRDCMBoost modes, the starting instant of the switching
pattern is aligned with the rising edge of the positive 𝑣AB at
𝑖p=0, as depicted in Fig. 7. Thereby, the initial and ending
steadystate currents in these modulation modes are always
zero, which inherently avoids a transient dcbias current.
A. PredictiveCurrent SinglePhaseShift for Smooth Mode
Transitions
Different from the CCM and DCM modes, the SPS mod
ulation usually does not have a ZCS turnoff instant of
switches except for the ZVS boundary condition. To enable a
smooth mode transition without a transient dcbias current, the
starting instant of the switching pattern needs to be determined
by predicting the zerocrossing of the transformer current.
Fortunately, as depicted in Fig. 10(a), the zerocrossing of 𝑖pis
always in the phaseshift interval between the rising edges of
𝑣AB and 𝑣CD, since only the ZVS region of the SPS modulation
is considered in the proposed method. Based on the derived
expression of the piecewise linear current [2], the time interval
𝑡xbetween the rising edge of 𝑣AB and the current zerocrossing
can be calculated by
𝑡x=
4𝑑𝐷 𝜑+1−𝑑
4(1+𝑑)𝑓.(20)
By delaying the starting instant of the switching pattern with a
time interval of 𝑡xfrom the rising edge of 𝑣AB, the initial and
DAB
Vs
Vs
*
PI
Vs
Vp
Mode selection &
Calculate control
parameters
Pulse
generator
Dφ
Dp
Ds
Iload
Iout
Fig. 11: Generalized closedloop control block diagram for the DAB converter.
Update Parameter:
d, VP,and Is,dc ≥0
Boundary calculation:
Is,dc,max,1
for SPS with (2)
Is,dc,max,2
for TZCCMBuck with (9a)
Is,dc,max,3
for TRDCMBuck with
Is,dc,max,4
for TZCCMBoost with (15a)
Is,dc,max,5
for TRDCMBoost with (18a)
SPS
Dφ= 0.25
Dp= 0.5
Ds= 0.5
SPS
Dφwith (3)
Dp= 0.5
Ds= 0.5
Is,dc <Is,dc,max,1
TZCCMBoost
Dφ
Dp= 0.5
Ds
Is,dc <Is,dc,max,4
TRDCMBuck
Dφwith ( )
Dp=dDs
Ds= 2Dφ/(1

d)
Is,dc <Is,dc,max,3
TZCCMBuck
Dφwith ( )
Dp
Ds= 0.5
Is,dc <Is,dc,max,2
TRDCMBoost
Dφ
Dp=dDs
Ds= 2Dφ/(d1)
Is,dc <Is,dc,max,5
Yes
No
Yes
No
No
Yes
Yes
Yes
No
No
with ( )
with ( )
(11a)
12 19 6
with ( )
8
13
with ( )
16
Fig. 12: Flowchart of the modelbased feedforward function.
ending steadystate currents of the SPS modulation are also
zero, as depicted in Fig. 10(a). Thus, the DAB converter can
inherently realize a dynamic current control and smooth mode
transitions as shown in Fig. 10(b). Compared to other methods
that suppress the induced transient dcbias current [26]–[30],
the proposed modulation methods inherently avoids this issue,
which improves the transient performance with minimized
computational efforts.
B. Uniﬁed HybridMode Voltage Control
The proposed hybridmode modulation strategy can be
implemented in a generalized closedloop voltage controller, as
depicted in Fig. 11. The output dc voltage is simply controlled
by a PI regulator, which generates a reference output dc cur
rent. With the derived closedform solutions for the modulation
modes in Section II, a modelbased feedforward function is
constructed, which selects the suitable modulation mode and
directly calculates the corresponding control variables based
on the measured dc voltage ratio and reference output dc
current. Such kind of modelbased feedforward control is
beneﬁcial to improve the dynamic performance of the DAB
converter [37]. Fig. 12 presents the ﬂowchart of the model
based feedforward function. As depicted in Fig. 11, the feed
forward path of 𝐼load can be implemented to constitute the
reference output dc current together with the output of the
voltage PI regulator. Thereby, the closedloop control has a
better capability of rejecting the load disturbance, leading
to a faster load transient response. Notice that the steady
state switching pattern of each mode is precalculated with
zero initial current as illustrated in Section IIIA, a dedicated
dynamic controller to calculate the transient switching pattern
is no longer required.
IEEE POWER ELECTRONICS REGULAR PAPER 7
(a) (b)
Output DC Voltage
Inductor current
39.6
39.8
40.0
Time in second
0.18 0.20 0.22 0.24 0.26 0.28
10
0
10
Output DC Voltage
Inductor current
39.7
39.8
39.9
40.0
× 1e1
Time in second
1.998 2.000 2.002 2.004
10
0
10
Current in A Voltage in V
Current in A Voltage in V
No mismatch
Lσ,actual=1.2Lσ
No mismatch
Lσ,actual=1.2Lσ
Fig. 13: Simulation results of a load step response with the proposed
control method considering tolerance in the leakage inductance. Simulation
parameters are 𝑉p=80 V,𝑉s=40 V,𝑁tr =1,𝑓=20 kHz,𝐿𝜎=39 µH,
output capacitance 𝐶out =1 mF, proportional gain 𝐾P=0.83 and integral
gain 𝐾I=34.74. (a) Fulltime view. (b) Zoomin view.
C. Discussion on Parameter Tolerance and Nonlinearities
As the proposed current control is based on feedforward
functions, the parameter tolerance particularly in the induc
tance value can inﬂuence the operation of the DAB converter.
Take the TRDCMBuck mode as an example, the phaseshift
ratio 𝐷𝜑,calc is calculated based on the reference output dc
current 𝐼s,dc,ref and the leakage inductance 𝐿𝜎according to
(12).
𝐷𝜑,calc =(1−𝑑)𝑓 𝐿 𝜎𝐼s,dc,ref
4𝑑𝑁tr𝑉p
(21)
Assuming the actual leakage inductance is 𝐿𝜎 ,actual =𝑘·𝐿𝜎
with a scaling factor 𝑘, it yields to an actual output dc current
by substituting (21) in (10),
𝐼s,dc,actual =
4𝑁tr𝑉p𝑑𝐷2
𝜑,calc
(1−𝑑)𝑓 𝐿 𝜎,actual
=
𝐼s,dc,ref
𝑘,(22)
which is scaled by 1
/𝑘compared to the reference value.
This introduces an error of (1−1
/𝑘)𝐼s,dc,ref in the output
dc current. Due to the existence of the voltage PI regulator
in the controller as shown in Fig. 11, the reference output
dc current 𝐼s,dc,ref will be adapted to compensate the error
caused by the leakage inductance. Therefore, the dynamic
response of the DAB converter will be clearly slower with a
tolerance in the leakage inductance, as shown in the simulation
result in Fig. 13(a). However, since the relationships of control
variables 𝐷𝜑,𝐷pand 𝐷sare independent from the leakage
inductance in the proposed method, the triangular inductor
current with ZCS turnoff can still be realized even with a
tolerance in the leakage inductance, as shown in Fig. 13(b).
Moreover, it is worth mentioning that the accurate parameter
of the leakage inductance in the DAB converter can be
identiﬁed online using the method proposed in [38]. Thereby,
the model parameter can be continuously updated to improve
the dynamic response of the DAB converter.
It should be also mentioned that the nonlinearties such as
dead time and parasitic capacitance have some impacts on
the instant current calculations, which can be addressed with
dedicated methods. In [39], the dead time can be effectively
compensated in the triangular and trapezoidal modulation to
mitigate the distortion effect. The parasitic capacitance can
be compensated by the chargebased modulation as proposed
in [40], which, however, inevitably increases the computational
XRS 7070 RealTime
Simulator/Controller
DAB #1
Device under Test DAB #2
DC Source
Adapter boards
Fig. 14: Experiment setup.
Parameter Value
Input dc voltage 80 V
Total leakage inductance 39 µH
Transformer turns ratio 1:1
Switching frequency 20 kHz
Output capacitance 1 mF
Dead time 1.0µs
TABLE II: Experimental parameters.
efforts. Another possible approach is to compensate the non
linear effects in the trapezoidal and triangular modulation by
empirically correcting the switching timings according to [41],
which requires parameter tuning through experiments.
IV. EXP ER IM EN TAL VERIFICATIO N
A smallscale DAB converter prototype, as shown in Fig. 14,
is built to verify the proposed modulation and control methods.
Detailed parameters of the prototype are given in Table II.
A second DAB converter with the same speciﬁcations is
employed to circulate the power in the experiments. The input
voltage is always ﬁxed to 80 V. An XRS 7070 realtime
controller from AixControl is employed for the experimental
implementation, which is internally based on a DSP+FPGA
architecture. Considering the simple switching patterns and
the fair computational complexity, the proposed control can
also be easily implemented on other control platforms such as
commercial DSPs or FPGAs with DSP slices.
A. Comparison with the SAB Operation
Fig. 15(a) shows the calculated operation boundary of the
hybridmode modulation for the converter prototype. At a
ﬁxed voltage ratio 𝑑=0.5, the output dc current is gradually
increased to identify the boundaries of operation modes in both
the SAB operation and the proposed hybridmode modulation.
Fig. 15(b)(e) show the operation waveforms of four operation
points P1P4, which correspond to the TRDCMBuck mode
with 𝐼s,dc =4 A, the boundary condition between the TR
DCMBuck and the TZCCMBuck modes with 𝐼s,dc =6.7 A,
the TZCCMBuck mode with 𝐼s,dc =8 A, and the boundary
condition between the TZCCMBuck and the SPS modes with
𝐼s,dc =9.5 A, respectively. It is shown that the waveforms
of the DAB converter match very well with the SAB con
verter in different operation modes, where the triangular and
trapezoidal transformer current with ZCS turnoff of switches
are realized. Besides, the natural boundary transitions between
the modulation modes are also veriﬁed, which coincide with
the theoretical analysis. Moreover, it can also be found in
Fig. 15(b) that the highfrequency oscillation of 𝑣CD in the
TRDCMBuck mode of the SAB converter is successfully
eliminated by the DAB operation. As shown in Fig. 15(f),
compared to the SAB operation, the efﬁciency of the DAB
converter with the proposed modulation increases by 2−2.7 %
over the whole load range at 𝑑=0.5due to the synchronous
rectiﬁcation.
B. SteadyState Performance
Furthermore, the steadystate performance of the proposed
method is compared with the conventional SPS modulation,
IEEE POWER ELECTRONICS REGULAR PAPER 8
μ
(a) (b)
(c) (d)
(e) (f)
P1
P2
P3
P4
μμ
μ
Fig. 15: Comparison of the SAB operation and the proposed hybridmode
modulation. (a) Operation boundary of the DAB prototype; (b) Experimental
waveforms of the TRDCMBuck mode at point P1; (c) Experimental wave
forms of the boundary condition between TRDCMBuck and TZCCMBuck
at point P2; (d) Experimental waveforms of the TZCCMBuck mode at point
P3; (e) Experimental waveforms of the boundary condition between TRCCM
Buck and SPS at point P4; (f) Measured efﬁciency curves at 𝑑=0.5.
the FOPS modulation [17] and the optimal TPS modula
tion [24] under different operation conditions. Fig. 16 shows
the operation waveforms at 𝑉s=60 V and 𝐼s,dc =1 A, which
correspond to the hardswitching operation in the SPS mod
ulation as well as the TRDCMBuck mode in the proposed
method. Although softswitching can also be realized by the
FOPS modulation as depicted in Fig.16(b), the transformer
rms current is obviously larger than the TRDCMBuck mode.
Moreover, the proposed modulation yields the same switching
pattern as the optimal TPS modulation as shown in Fig. 16(c)
and (d). Fig. 17 shows the operation waveforms at 𝑉s=40 V
and 𝐼s,dc =8 A, which corresponds to the TZCCMBuck
mode in the proposed method. This operating point is beyond
the operation range of the FOPS modulation. It is shown that
the optimal TPS modulation and the proposed TZCCMBuck
mode can realize ZVS and ZVS/ZCS operation, respectively,
with comparable rms currents. Fig. 18 and Fig. 19 further show
the operation waveforms in the boost mode at 𝑉s=100 V with
𝐼s,dc =2 A and 𝐼s,dc =4.7 A, respectively. In these two cases,
both the SPS modulation and FOPS modulation suffer from
hardswitching. Meanwhile, the DAB converter operates in the
TRDCMBoost and TZCCMBoost modes in the proposed
method, respectively, which realize ZVS/ZCS operation via
the triangular or trapezoidal current. From both the optimal
TPS modulation and the proposed method, it can be found
that the triangular inductor current results in the lowest rms
value in the lowpower range. Although ZCS turnoff can
avoid the diode reverse recovery, there is still turnon loss due
C7 C7
(a) (b)
(c)
vAB: 20V/div
(d)
C7
vAB: 20V/div vCD: 20V/div
ip: 5A/div
10μs/div Ip,rms=1.71A
C7
vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
10μs/div 10μs/div
10μs/div
Ip,rms=4.24A Ip,rms=2.63A
Ip,rms=1.71A
Fig. 16: Measured waveforms at 𝑉s=60 V and 𝐼s,dc =1 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(d) Proposed method (TRDCMBuck).
(c)
(a) (b)
C7
10μs/div
C7
vAB: 20V/div
vCD: 20V/div ip: 5A/div
10μs/div
C7
10μs/div
vAB: 20V/div
vCD: 20V/div ip: 5A/div
vAB: 20V/div
vCD: 20V/div ip: 5A/div
Ip,rms=9.68A Ip,rms=9.02A
Ip,rms=9.07A
Fig. 17: Measured waveforms at 𝑉s=40 V and 𝐼s,dc =8 A. (a) SPS
modulation; (b) Optimal TPS modulation [24]; (c) Proposed method (TZ
CCMBuck).
(a) (b)
(c) (d)
C7
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
Ip,rms=3.50A
C7 C7
C7
10μs/div 10μs/div
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
Ip,rms=4.32A Ip,rms=3.83A
Ip,rms=3.50A
Fig. 18: Measured waveforms at 𝑉s=100 V and 𝐼s,dc =2 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(c) Proposed method (TRDCMBoost).
to the charge of the device output capacitance. In practice,
the magnetizing current of the transformer can contribute an
additional inductive current to assist the charging/discharging
process of the output capacitance.
The converter efﬁciency is also measured and compared
among the four modulation methods over a wide operating
range. As shown in Fig. 20(a), at 𝑑=0.5, the optimal TPS
IEEE POWER ELECTRONICS REGULAR PAPER 9
Ip,rms=7.02A Ip,rms=6.86A
Ip,rms=6.81A
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
(a) (b)
(d)
(c)
10μs/div 10μs/div
C7
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
10μs/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
vAB: 20V/div vCD: 20V/div
ip: 5A/div
C7
10μs/div Ip,rms=6.79A
Fig. 19: Measured waveforms at 𝑉s=100 V and 𝐼s,dc =4.7 A. (a) SPS
modulation; (b) FOPS modulation [17]; (c) Optimal TPS modulation [24];
(d) Proposed method (TZCCMBoost).
Efficiency in %
Efficiency in %
Efficiency in %
(a) (b)
(c)
Fig. 20: Measured efﬁciency curves of the SPS, the FOPS [17], the optimal
TPS [24] and the proposed modulation method. (a) 𝑉s=40 V, i.e. 𝑑=0.5;
(b) 𝑉s=60 V, i.e. 𝑑=0.75; (c) 𝑉s=100 V, i.e. 𝑑=1.25.
modulation shows the highest efﬁciency over the whole load
range from 1 A to 10 A, with the peak value of 94.2 % at
𝐼s,dc =2 A. Compared to the optimal TPS modulation, the
proposed method shows a very close performance with the
same peak efﬁciency and a slightly lower efﬁciency with a
difference less than 0.2 % in the medium to high load range.
Compared to the SPS modulation, the efﬁciency improvement
of the proposed method is up to 30.3 %. Besides, the proposed
method also achieves a higher efﬁciency than the FOPS
modulation due to the reduced rms current. Similar results
are also observed from Fig. 20(b) with 𝑑=0.75, which
verify the signiﬁcant efﬁciency improvements of the proposed
method under lightload conditions. It is also found that,
with an increasing load current, the efﬁciency of the SPS
modulation becomes even higher than the FOPS modulation
due to the reduced rms current. Fig. 20(c) further shows the
efﬁciency curve at 𝑑=1.25. In this case, the proposed method
and the optimal TPS modulation share the highest lightload
efﬁciency, which is up to 8.6 % and 5.7 % higher than the
SPS modulation and the FOPS modulation, respectively. When
the SPS modulation is selected in the proposed method at
TRDCMBuck
TZCCMBuck
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
: ZVSon : ZCSoff
Fig. 21: Measured transient waveforms with the operationmode change from
the TRDCMBuck mode with 𝐼s,dc =3 A to the TZCCMBuck mode with
𝐼s,dc =9 A at 𝑉s=40 V.
40μs/div
TRDCMBuck
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
40μs/div
TRDCMBuck
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
(a)
(b)
transient overshoot
: ZVSon : ZCSoff
Fig. 22: Measured transient waveforms with the operationmode change from
the TRDCMBuck mode with 𝐼s,dc =3 A to the SPS mode with 𝐼s,dc =7 A at
𝑉s=60 V. (a) Conventional SPS modulation; (b) Proposed predictivecurrent
SPS modulation.
𝐼s,dc ≥5 A, the FOPS modulation shows a slightly improved
efﬁciency with less than 0.5 %.
In conclusion, the steadystate performance of the proposed
modulation is very close to the optimal TPS modulation [24],
which is signiﬁcantly improved compared to the conventional
SPS and the FOPS modulation [17]. However, it should be
noticed that the optimal TPS modulation requires a complex
optimization algorithm to derive the optimal control parame
ters, while the proposed method is intuitively derived from the
simple SAB operation without any optimization procedure.
C. LoadTransient Performance
The performance of the inherent dynamic control with
the proposed hybridmode modulation is validated in load
IEEE POWER ELECTRONICS REGULAR PAPER 10
(b)
40μs/div
TRDCMBoost
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
(a)
40μs/div
TRDCMBoost
SPS
vAB: 50V/div vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 20V/div
: ZVSon : ZCSoff
transient overshoot
Fig. 23: Measured transient waveforms with the operationmode change from
the TRDCMBoost mode with 𝐼s,dc =3 A to the SPS mode with 𝐼s,dc =8 A
at 𝑉s=100 V. (a) Conventional SPS modulation; (b) Proposed predictive
current SPS modulation.
is,dc: 5A/div
vAB: 50V/div vCD: 50V/div ip: 10A/div
transient overshoot
Fig. 24: Measured transient waveforms of the optimal TPS modulation [24]
from 𝐼s,dc =3 A to 𝐼s,dc =9 A at 𝑉s=40V.
transient tests. In Fig. 21, a step change of the load current
from 3 A to 9 A occurs at 𝑉s=40 V, which results in a
smooth transition from the TRDCMBuck to the TZCCM
Buck mode without a noticeable transient dcbias current.
Meanwhile, ZVS turnon and ZCS turnoff operation can also
be veriﬁed in the transient waveforms. Furthermore, Fig. 22
shows a step change of the load current from 3 A to 7 A occurs
at 𝑉s=60 V, where the operation mode changes from the TR
DCMBuck to the SPS mode. Compared to the situation with
the conventional SPS modulation as shown in Fig. 22(a), the
proposed predictivecurrent SPS modulation enables a smooth
mode transition without a transient dcbias current as shown
in Fig. 22(b). Similar results are observed in Fig. 23, when
the load current changes from 3 A to 8 A at 𝑉s=100 V. The
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
is,dc: 5A/div
Vs: 50V/div
200ms/div
SPS SPS
TRDCMBuck
TZCCMBuck
Vs=100V
Vs=10V
20μs/div
TRDCMBuck
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
20μs/div
TZCCMBuck
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div
vCD: 50V/div
ip: 10A/div
20μs/div
SPS
is,dc: 5A/div
Vs: 50V/div
vAB: 50V/div vCD: 50V/div
ip: 10A/div
(a)
(b)
(c)
(d)
Fig. 25: Measured transient waveforms with ramp changes of the reference
output dc voltage from 100 V to 10 V at a constant load current of 𝐼s,dc =
5.5 A. (a) Wholeprocess waveforms; (b) Zoomedin waveforms of the TR
DCMBuck mode; (c) Zoomedin waveforms of the TZCCMBuck mode;
(d) Zoomedin waveforms of the predictivecurrent SPS mode.
operation mode changes from the TRDCMBoost to the SPS
mode. It is shown that the predictivecurrent SPS modulation
is also effective to avoid a transient dcbias current in the boost
IEEE POWER ELECTRONICS REGULAR PAPER 11
mode. Therefore, it is veriﬁed that the proposed hybridmode
modulation realizes inherent dynamic control with smooth
mode transitions under loadtransient conditions.
In contrast, a large transient overshoot current is induced
under the load transient condition with the optimal TPS
modulation [24], as shown in Fig. 24, which takes a few
switching cycles to decay.
D. WideRange Voltage Control
The proposed hybridmode modulation enables an ultra
widevoltagerange operation, which is crucial in many ap
plications such as black startup and lowvoltage ride through.
Fig. 25 shows the transient waveforms of the DAB converter
operating in the voltage control mode with the proposed
hybridmode modulation. As shown in Fig. 25(a), the reference
output dc voltage ﬁrst ramps down from 100 V to 10 V with
a slope of −0.3 V/ms, and then remains constant at 10 V for
another 300 ms. Thereafter, the reference output dc voltage
ramps up back to 100 V with a slope of 0.3 V/ms. During the
whole transient process, the load current remains constant at
𝐼s,dc =5.5 A. It is shown that the output dc voltage is regulated
to successfully follow the reference even under the low
voltageratio condition, i.e. 𝑑=0.125. With the continuously
changing operating condition, the operation mode changes
smoothly in the sequence of SPS, TZCCMBuck, TRDCM
Buck, TZCCMBuck and SPS. Meanwhile, the transformer
current is well regulated without an obvious transient over
shoot. Moreover, it also veriﬁes that the DAB converter can
deliver the same output dc current under the ultralowvoltage
condition without increasing the current stress of devices.
Fig. 25(b)(d) further show the zoomedin waveforms of the
TRDCMBuck, TZCCMBuck and SPS modes, respectively,
which validate the effectiveness of the proposed modulation
in the voltage control mode.
E. Comparison of Modulation Methods
Based on the previous analysis and experimental validations,
the beneﬁts and constraints of the proposed hybrid modulation
can be summarized in Table III compared to several stateof
theart modulation methods. Compared to the SPS, FOPS [17]
and conventional trapezoidal and triangular modulation [41],
the proposed hybrid modulation and the optimal TPS modu
lation [24] have more control variables to realize ZVS/ZCS
softswitching in the full operating range. Although the op
timal TPS modulation [24] results in a globally optimized
RMS current, the optimization procedure of control param
eters requires complex calculations. In contrast, the proposed
modulation is derived intuitively from the SAB operation
which has simple closedform solutions and does not require
any complex optimization process. Moreover, compared to
the other modulation methods including the optimal TPS,
the proposed modulation can inherently realize smooth mode
transitions without transient overshoot currents. This leads
to a simple implementation of the closedloop control with
suppressed transients.
TABLE III: Qualitative comparison of different modulation methods.
Mode Number of
variables
Softsw.
range
Type of
softsw. RMS current Optimization
complexity
Suppressed
transients
SPS [1] 1 Partial ZVS Nonoptimal None No
FOPS [17] 2 Partial
(improved) ZVS Suboptimal Medium No
Trapezoidal and
Triangular
modulation [41]
3Partial
(improved) ZVS/ZCS Suboptimal Low Yes
Optimal TPS [24] 3 Full ZVS/ZCS Optimal High No
Proposed method 3 Full ZVS/ZCS Suboptimal None Yes
V. CONCLUSION
In this article, a hybridmode modulation strategy with
natural boundary transitions and inherent dynamic control
is proposed for the singlephase DAB converter. Inspired
by the quasisingleactivebridge operation, four dedicated
modulation modes with the trapezoidal and triangular current
waveforms are intuitively derived, which can naturally and
sequentially extend the softswitching boundary of the SPS
modulation to the full operating range with a reduced rms
current. Moreover, with the predictivecurrent SPS modulation,
zero initial steadystate transformer current is realized in each
of the modulation modes. This enables inherent dynamic
control and smooth mode transitions without any dedicated
transientcurrent control strategy. The proposed hybridmode
modulation with closedform solutions is implemented in a
uniﬁed voltage controller, which allows the DAB converter to
operate in an ultrawide voltage range with improved overall
efﬁciency and a fast transient response. The effectiveness
of the proposed modulation and control methods has been
validated by comprehensive experiments on a smallscale DAB
converter prototype.
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IEEE POWER ELECTRONICS REGULAR PAPER 13
Jingxin Hu (Member, IEEE) received the B.S. de
gree from Northeastern University, Shenyang, China,
in 2010, and the M.Sc. and Dr.Ing. degrees, with the
highest distinction (summa cum laude), from RWTH
Aachen University, Aachen, Germany, in 2013 and
2019 respectively, all in electrical engineering.
From April to October 2012, he was a research
intern with the ABB Corporate Research Center,
BadenD¨
attwil, Switzerland. In 2013, he joined the
General Electric Global Research Center, Munich,
Germany. Since October 2014, he has been with
the Institute for Power Generation and Storage Systems, E.ON Energy
Research Center, RWTH Aachen University, where he is currently a Senior
Scientist. Since February 2021, he is also the Research Project Leader at
FEN GmbH, Germany. His research interests include power electronics, solid
state transformers, MVDC and LVDC distribution systems and applications
of widebandgap devices.
Dr. Hu was the recipient of the RWTH Aachen  University of Alberta
Senior Research Fellowship in 2021, the STAWAG Best Dissertation Prize
of RWTH Aachen University in 2019, the Chinese Government Award for
Outstanding SelfFinanced Students Abroad in 2019, and the Second Prize
Paper Award of IEEE IPEC (ECCE Asia) in 2018.
Shenghui Cui (Member, IEEE) received the B.S.
degree from Tsinghua University, Beijing, China, in
2012, the M.S. degree from Seoul National Uni
versity, Seoul, South Korea, in 2014, and the Dr.
Ing. degree with the highest distinction (summa
cum laude) from RWTH Aachen University, Aachen,
Germany, in 2019, all in electrical engineering.
Since September 2021, Dr. Cui is with Depart
ment of Electrical and Computer Engineering, Seoul
National University, Seoul, South Korea as an Assis
tant Professor. From March 2015 to May 2021, he
has been with the Institute for Power Generation and Storage Systems, E.ON
Energy Research Center, RWTH Aachen University, Aachen, Germany, where
he worked as Research Associate and later on Senior Scientist. His research
interests include interaction of power systems and power converters, power
converters in ac/dc utility applications, and applications of wideband gap
power devices.
Dr. Cui was the recipient of the STAWAG Best Dissertation Prize from
Faculty of Electrical Engineering and Information Technology, RWTH Aachen
University in 2019, the Second Place Prize Paper Award of the IEEE
Transactions on Power Electronics in 2018, the Second Prize Paper Award of
IEEE IPEC (ECCE Asia) in 2018, and the Outstanding Presentation Award
of the IEEE Applied Power Electronics Conference in 2014.
Rik W. De Doncker (Fellow, IEEE) received
the Ph.D. degree in electrical engineering from
Katholieke Universiteit Leuven, Leuven, Belgium,
in 1986.
In 1987, he was a Visiting Associate Professor
with the University of WisconsinMadison, Madison,
WI, USA, in 1988, a Senior Scientist with GE
CR&D, Schenectady, NY, USA, and in 1994, Vice
President Technology of SPCO, developing world’s
ﬁrst MVSTS. Since October 1996, he has been a
Professor with RWTH Aachen University, Aachen,
Germany, leading the Institute for Power Electronics and Electrical Drives.
In 2006, he became the Director of E.ON ERC, RWTH and founded the
Institute for Power Generation and Storage Systems. He leads the RWTH
CAMPUS Cluster Sustainable Energy and the BMBF Flexible Electrical
Networks Research CAMPUS. Since 2010, he has been a Member of the
German National Platform for Electric Mobility, since 2017, of the French
VEDECOM, and since 2016, of the German Academy of Science and
Technology.
He was the recipient of the IEEE IAS Outstanding Achievements Award,
the PES Nari Hingorani Custom Power Award in 2008, the 2013 Newell
Power Electronics Field Award, the 2014 IEEE PELS H. Owen Outstanding
Service Award, RWTH Fellow status in 2015, and the IEEE Gold Medal in
Power Engineering in 2020.